Download PDF - A note on the strong consistency of least squares estimatesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A note on the strong consistency of least squares estimates

Authors 1

Affiliations

  1. Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

Abstract

The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.

Keywords

ENG
least squares estimates, linear models, strong consistency

Bibliography

  1. [1] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales (third edition) Springer 1997.
  2. [2] Chen Xiru, Consistency of LS estimates of multiple regression under a lower order moment condition, Sci. Chin. 38 (12) (1995), 1420-1431.
  3. [3] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press 1985.
  4. [4] H. Drygas, Consistency of the least squares and Gauss-Markov estimators in regression models, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17 (1971), 309-326.
  5. [5] H. Drygas, Weak and strong consistency of the least squares estimators in regression model, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 34 (1976), 119-127.
  6. [6] C. Gui-Jing, T.L. Lai and C.Z. Wei, Convergence systems and strong, consistency of least squares estimates in regression models, J. Multivariate Anal. 11 (1981), 319-333.
  7. [7] C. GuiJing, Extension of Lai-Robbins-Wei's theorem, Acta Mathematicae Applicatae Sinica 1 (1) (1984), 2-7.
  8. [8]J. Mingzhong, Some new results of the strong consistency of multiple regression coefficients, in: S. Tangmanee & E. Schulz, eds. World Scientific, Proceedings of the Second Asian Mathematical Conference 1995 (R. Nakhon 1995), 514-519.
  9. [9] T.L. Lai, H. Robbins and C.Z. Wei, Strong consistency of least squares estimates in multiple regression II, J. Multivariate Anal. 9 (1979), 343-362.
  10. [10] B.M. Makarov, M.G. Goluzina, A.A. Lodkin and A.N. Podkorytov, Selected Problems in Real Analysis (American Mathematical Society, Providence R.I. 1992).
  11. [11] J.T. Mexia, P. Corte Real, M.L. Esquível e J. Lita da Silva, Convergência do estimador dos mínimos quadrados em modelos lineares, Estatística Jubilar. Actas do XII Congresso da Sociedade Portuguesa de Estatística, Edições SPE (2005), 455-466.
  12. [12] J.T. Mexia e J. Lita da Silva, A consistência do estimador dos mínimos quadrados em domínios de atracção maximais, Ciência Estatística. Actas do XIII Congresso Anual da Sociedade Portuguesa de Estatística, Edições SPE (2006), 481-492.
  13. [13] J.T. Mexia and J. Lita da Silva, Sufficient conditions for the strong consistency of least squares estimator with α-stable errors, Discussiones Mathematicae - Probability and Statistics 27 (2007), 27-45.
Discussiones Mathematicae Probability and Statistics
2009/29/2
Export to PBN, Opens in new tab
Pages:
223-231
Main language of publication
English
Received
2009-11-15
Published
2009

DOI: 10.7151/dmps.1116

Exact and natural sciences